A stone is dropped from a ballon while ascending at the rate of 8mps. The stone reaches the ground in 6 sec. What is the height of the balloon when the stone was dropped?
h = Vo*t + 0.5g*t^2 = -8*6 + 4.9*6^2 =
128.4 m.
To find the height of the balloon when the stone was dropped, we can use the formula for the distance traveled by an object under constant acceleration:
š = š¢š” + 0.5šš”Ā²
where š is the distance traveled, š¢ is the initial velocity, š” is the time taken, and š is the acceleration.
In this case, the stone is dropped from the balloon, so its initial velocity is 0 m/s, and the acceleration due to gravity is -9.8 m/sĀ² (negative because it is acting opposite to the direction of motion).
Given that the stone reaches the ground in 6 seconds, we can substitute these values into the formula:
š = 0 Ć 6 + 0.5 Ć (-9.8) Ć (6)Ā²
š = -0.5 Ć 9.8 Ć 36
š = -0.5 Ć 352.8
š = -176.4
The negative sign indicates that the stone is moving in the opposite direction to the conventionally positive direction (upward in this case).
Therefore, the height of the balloon when the stone was dropped is 176.4 meters below the reference point.